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Results for “probability generating function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Probabilistic #D data fusion for multiresolution surface generation

In this paper we present an algorithm for adaptive resolution integration of 3D data collected from multiple distributed sensors. The input to the algorithm is a set of 3D surface points and associated sensor models. Using a probabilistic rule, a surface probability function is generated that represents the probability that a particular volume of space contains the surface. The surface probability function is represented using an octree data structure; regions of space with samples of large conariance are stored at a coarser level than regions of space containing samples with smaller covariance. The algorithm outputs an adaptive resolution surface generated by connecting points that lie on the ridge of surface probability with triangles scaled to match the local discretization of space given by the algorithm, we present results from 3D data generated by scanning lidar and structure from motion.

3D data fusion multiresolution surface generation ↗
NASA NTRS1995

A LEO concept for millimeter wave satellite communication

A conceptual 60 satellite LEO constellation for millimeter wave communication is discussed. It could be launched in segments, with the first 30 satellites providing high elevation angles for all time in the Northern latitudes between Miami and Thule. The second set of 30 satellites would complete the worldwide coverage with emphasis on high ground elevation angles in the densely populated temperate zones. Full earth searches for all time are used to generate probability density functions for elevation angle. The density functions are used to derive optimum frequencies for random elevation systems. The 55 degree average elevation angle and 14 degree standard deviation are seen to be acceptable for 0.997 rain availability in Washington, DC for the 40 to 47 GHz region. The 40 to 47 GHz region is nearly optimum, if 0.99 rain availability is acceptable.

Jackson, A. H.↗
NASA NTRS1971

Opacity probability distribution functions for electronic systems of CN and C2 molecules including their stellar isotopic forms.

The basis and techniques are presented for generating opacity probability distribution functions for the CN molecule (red and violet systems) and the C2 molecule (Swan, Phillips, Ballik-Ramsay systems), two of the more important diatomic molecules in the spectra of carbon stars, with a view to including these distribution functions in equilibrium model atmosphere calculations. Comparisons to the CO molecule are also shown. T he computation of the monochromatic absorption coefficient uses the most recent molecular data with revision of the oscillator strengths for some of the band systems. The total molecular stellar mass absorption coefficient is established through fifteen equations of molecular dissociation equilibrium to relate the distribution functions to each other on a per gram of stellar material basis.

Querci, F.↗
NASA NTRS1988

Probabilistic constitutive relationships for cyclic material strength models

A methodology is developed that provides a probabilistic treatment for the lifetime of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs.

Boyce, L.↗
NASA NTRS1989

Probabilistic analysis for fatigue strength degradation of materials

This report presents the results of the first year of a research program conducted for NASA-LeRC by the University of Texas at San Antonio. The research included development of methodology that provides a probabilistic treatment of lifetime prediction of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Linear elastic fracture mechanics is utilized in the latter model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs, RANDOM2, RANDOM3, and RANDOM4. These programs determine the random lifetime of an engine component, in mechanical load cycles, to reach a critical fatigue strength or crack size. The material considered was a cast nickel base superalloy, one typical of those used in the Space Shuttle Main Engine.

Royce, Lola↗
NASA NTRS1972

Investigation of estimators of probability density functions

Four research projects are summarized which include: (1) the generation of random numbers on the IBM 360/44, (2) statistical tests used to check out random number generators, (3) Specht density estimators, and (4) use of estimators of probability density functions in analyzing large amounts of data.

Speed, F. M.↗
NASA NTRS1988

Performance evaluation of fault-tolerant systems with application to the IUS

A new method for quantitatively evaluating the performance of fault-tolerant systems is developed and applied to an example. The method assumes that the random failure and diagnostic decision behavior of the system can be modeled by a finite state Markov process. A performance value must be assigned to each of the states of the model. The method then generates the moments of the probability mass function of the cumulative performance and uses these to generate a maximum entropy approximation to the performance PMF. Some computational considerations are discussed. The method is applied to a typical mission for the Inertial Upper Stage to examine the attitude accuracy performance of the inertial system.

Missana, J.-O.↗
NASA NTRS1971

Reward and uncertainty in exploration programs

A set of variables which are crucial to the economic outcome of petroleum exploration are discussed. These are treated as random variables; the values they assume indicate the number of successes that occur in a drilling program and determine, for a particular discovery, the unit production cost and net economic return if that reservoir is developed. In specifying the joint probability law for those variables, extreme and probably unrealistic assumptions are made. In particular, the different random variables are assumed to be independently distributed. Using postulated probability functions and specified parameters, values are generated for selected random variables, such as reservoir size. From this set of values the economic magnitudes of interest, net return and unit production cost are computed. This constitutes a single trial, and the procedure is repeated many times. The resulting histograms approximate the probability density functions of the variables which describe the economic outcomes of an exploratory drilling program.

Kaufman, G. M.↗
NASA NTRS1980

An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

Huang, N. E.↗
NASA NTRS2007

Uncertainty Management for Diagnostics and Prognostics of Batteries using Bayesian Techniques

Uncertainty management has always been the key hurdle faced by diagnostics and prognostics algorithms. A Bayesian treatment of this problem provides an elegant and theoretically sound approach to the modern Condition- Based Maintenance (CBM)/Prognostic Health Management (PHM) paradigm. The application of the Bayesian techniques to regression and classification in the form of Relevance Vector Machine (RVM), and to state estimation as in Particle Filters (PF), provides a powerful tool to integrate the diagnosis and prognosis of battery health. The RVM, which is a Bayesian treatment of the Support Vector Machine (SVM), is used for model identification, while the PF framework uses the learnt model, statistical estimates of noise and anticipated operational conditions to provide estimates of remaining useful life (RUL) in the form of a probability density function (PDF). This type of prognostics generates a significant value addition to the management of any operation involving electrical systems.

Saha, Bhaskar↗
NASA NTRS1983

Sensory redundancy management: The development of a design methodology for determining threshold values through a statistical analysis of sensor output data

Sensor redundancy management (SRM) requires a system which will detect failures and reconstruct avionics accordingly. A probability density function to determine false alarm rates, using an algorithmic approach was generated. Microcomputer software was developed which will print out tables of values for the cummulative probability of being in the domain of failure; system reliability; and false alarm probability, given a signal is in the domain of failure. The microcomputer software was applied to the sensor output data for various AFT1 F-16 flights and sensor parameters. Practical recommendations for further research were made.

Scalzo, F.↗
NASA NTRS1994

Probability techniques for reliability analysis of composite materials

Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented.

Wetherhold, Robert C.↗
NASA NTRS1998

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗